Question

q5 simplify the expression.
\\(\frac{45y^{3}x}{5yx^{2}}\\)
options:
\\(\frac{9y^{2}}{x}\\)
\\(9y^{2}x\\)
\\(\frac{9y^{3}}{x^{2}}\\)

Explanation:

Step1: Simplify the coefficients

Simplify the fraction of the coefficients \(\frac{45}{5}\).
\(\frac{45}{5} = 9\)

Step2: Simplify the \(y\)-terms

Use the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\) for the \(y\)-terms \(\frac{y^{3}}{y}\).
\(\frac{y^{3}}{y}=y^{3 - 1}=y^{2}\)

Step3: Simplify the \(x\)-terms

Use the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\) for the \(x\)-terms \(\frac{x}{x^{2}}\).
\(\frac{x}{x^{2}}=x^{1 - 2}=x^{-1}=\frac{1}{x}\) (or we can think of it as \(\frac{x}{x^{2}}=\frac{1}{x}\) directly)

Step4: Combine the simplified terms

Multiply the simplified coefficient, \(y\)-term, and \(x\)-term together:
\(9\times y^{2}\times\frac{1}{x}=\frac{9y^{2}}{x}\)

Answer:

\(\frac{9y^{2}}{x}\) (corresponding to the first option: \(\boldsymbol{\frac{9y^{2}}{x}}\))